Pricing American options fitting the smile

This paper is a compendium of results-theoretical and computational-from a series of recent papers developing a new American option valuation techniqu e based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given , as is the analysis needed to solve the inverse problem of determining loc al (one-factor) volatility from market data. The ideas behind a fast accura te revised simplex method, whose performance is linear in time and space di scretizations, are described and the practicalities of fitting the volatili ty smile are discussed. Numerical results are presented which show the LP v aluation technique to be extremely fast-lattice speed with PDE accuracy. Am erican options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile.